Criterion of positivity for semilinear problems with applications in biology

Abstract : The goal of this article is to provide an useful criterion of positivity and well-posedness for a wide range of infinite dimensional semilinear abstract Cauchy problems. This criterion is based on some weak assumptions on the non-linear part of the semilinear problem and on the existence of a strongly continuous semigroup generated by the differential operator. To illustrate a large variety of applications, we exhibit the feasibility of this criterion through three examples in mathematical biology: epidemiology, predator-prey interactions and oncology.
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Soumis le : mardi 9 août 2016 - 10:03:34
Dernière modification le : samedi 18 novembre 2017 - 00:20:10

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Michel Duprez, Antoine Perasso. Criterion of positivity for semilinear problems with applications in biology. Positivity, Springer Verlag, 2017, 21 (4), p. 1383-1392. 〈10.1007/s11117-017-0474-0〉. 〈hal-01290966v2〉

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